3× pot overbet: pot odds, equity needed and MDF
What a bet of three times the pot asks of the caller and of the bettor, worked out exactly, with the formula and the numbers in it.
A bet of three times the pot is the near-shove that turns up when stacks are deep and the pot is small. Here is everything it asks, worked in units of the pot (P = 1, B = 3) and then in a 12 bb pot, where the bet is 36 bb.
pot odds (P + B) : B = 4 : 3 = 1.33 to 1 call needs B / (P + 2B) = 3 / 7 = 42.86% MDF P / (P + B) = 1 / 4 = 25.00% bluff must work B / (P + B) = 3 / 4 = 75.00% in a 12 bb pot: call 36 bb to win 48 bb; final pot 84 bb break-even equity = 36 bb / 84 bb = 42.86%
Can a draw call it?
Facing three times the pot on the turn, with one card to come, a draw needs at least 20 clean outs to call on the price alone (20 / 46 = 43.5% against 42.9% needed). On the flop, if the call only buys the turn, it needs 21; all-in on the flop, seeing both cards, it needs 12. A flush draw on the turn hits 19.6% of the time, so it is short, and must win about 8.33 pot more on the river when it hits (100 bb in a 12 bb pot).
| Draw | Facing a flop bet | Facing a turn bet | All-in on the flop |
|---|---|---|---|
| Gutshot (4) | 8.5% needs +28.25 pot | 8.7% needs +27.50 pot | 16.5% folds |
| Open-ended straight draw (8) | 17.0% needs +10.63 pot | 17.4% needs +10.25 pot | 31.5% folds |
| Flush draw (9) | 19.1% needs +8.67 pot | 19.6% needs +8.33 pot | 35.0% folds |
| Flush draw + gutshot (12) | 25.5% needs +4.75 pot | 26.1% needs +4.50 pot | 45.0% calls |
| Flush draw + open-ender (15) | 31.9% needs +2.40 pot | 32.6% needs +2.20 pot | 54.1% calls |
Green calls on the direct price. Red shows the implied odds still missing: the extra the draw must win when it hits, as a multiple of the pot before the bet. All-in there is nothing left to win, so a short draw folds.
Defending against it
A pure bluff of three times the pot risks 3 to win 1, so it profits if you fold more than 75.0% of the time. To stop any two cards from betting at a profit you have to continue with 25.0% of the range you arrived with: the minimum defence frequency. Defend ten points less, 15.0%, and every zero-equity bluff earns +0.40 pot on average:
bluff EV = fold × P − call × B = 0.850 × 1 − 0.150 × 3.000 = +0.40 pot
Betting it on the river
With a polarised range, nuts or air, the bettor makes a bluff-catcher indifferent by bluffing 3 / 7 of their bets, 42.9%. That is 4 : 3 value to bluffs, or about 7.5 bluff combos for every 10 value combos. The bluff share is the caller’s required equity again, which is the indifference: with P = 1 and B = 3, a bluff-catcher that calls wins 3 / 7 × 4 and loses 4 / 7 × 3, which are both 12 / 7 of a pot unit. See the bluff-to-value ratio for what happens either side of it.
Next to the other sizes
One size down, a 2× pot overbet asks for 40.0%. Bigger bets ask more of the caller, but never more than half: as B grows, B / (P + 2B) creeps towards 50% and never reaches it.
| Bet | Pot odds | Call needs | MDF | Bluff must work | River value : bluff | Outs to call a turn bet |
|---|---|---|---|---|---|---|
| Quarter-pot bet | 5 to 1 | 16.7% | 80.0% | 20.0% | 5 : 1 | 8 |
| Third-pot bet | 4 to 1 | 20.0% | 75.0% | 25.0% | 4 : 1 | 10 |
| Half-pot bet | 3 to 1 | 25.0% | 66.7% | 33.3% | 3 : 1 | 12 |
| Two-thirds-pot bet | 2.5 to 1 | 28.6% | 60.0% | 40.0% | 5 : 2 | 14 |
| Three-quarter-pot bet | 2.33 to 1 | 30.0% | 57.1% | 42.9% | 7 : 3 | 14 |
| Pot-sized bet | 2 to 1 | 33.3% | 50.0% | 50.0% | 2 : 1 | 16 |
| 1.5× pot overbet | 1.67 to 1 | 37.5% | 40.0% | 60.0% | 5 : 3 | 18 |
| 2× pot overbet | 1.5 to 1 | 40.0% | 33.3% | 66.7% | 3 : 2 | 19 |
| 3× pot overbet | 1.33 to 1 | 42.9% | 25.0% | 75.0% | 4 : 3 | 20 |
Every bet size
- Quarter-pot bet16.7%
- Third-pot bet20.0%
- Half-pot bet25.0%
- Two-thirds-pot bet28.6%
- Three-quarter-pot bet30.0%
- Pot-sized bet33.3%
- 1.5× pot overbet37.5%
- 2× pot overbet40.0%
The ideas behind the numbers
- The prices are exact. Pot odds, required equity, MDF and the bluff frequencies are arithmetic on the pot and the bet, printed as reduced fractions. Nothing is rounded until it is displayed.
- Draw odds are counted. The chance of hitting comes from the outs chart, which deals every turn and river. We assume clean outs: every out wins and nothing else does. Real draws are dirtier, and against a stated range the spot check counts the real equity instead.
- No rake, no future betting unless a page says otherwise. Implied odds are the one place we price a later street, and that page states its model.
- MDF and the river ratio are a toy game, not a solver output: a bettor with only the nuts or air, a caller with only bluff-catchers. They say what stops the other player profiting automatically. They are not a strategy for any single hand.